Ical
https://mathematics.huji.ac.il/calendar?type=month&month=term
en<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows?delta=0" >Kazhdan Sunday seminar: Elon Lindenstrauss "Arithmetic applications of diagonal flows" </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows
Elon Lindenstrauss "Arithmetic applications of diagonal flows"
I will give an introduction to the dynamics of higher rank diagonal flows on homogeneous spaces,
including both the rigidity theorems of such flows and their applications to orbits of arithmetic interest,
in particular CM points and integer points on spheres.
I hope to cover parts of the following papers:
Einsiedler, Manfred ; Lindenstrauss, Elon ; Michel, Philippe ; Venkatesh, Akshay . The distribution of closed geodesics
on the modular surface, and Duke's theorem. Enseign. Math. (2) 58 (2012), no. 3-4, 249--313.
Einsiedler, M., Lindenstrauss, E., Symmetry of entropy in higher rank diagonalizable actions and measure classification.
arXiv e-prints arXiv:1803.07762.
Einsiedler, M. & Lindenstrauss, E. .Joinings of higher rank torus actions on homogeneous spaces. Publ.math.IHES (2019).
<a href="https://doi.org/10.1007/s10240-019-00103-y">https://doi.org/10.1007/s10240-019-00103-y</a>
Khayutin, Ilya . Joint equidistribution of CM points. Ann. of Math. (2) 189 (2019), no. 1, 145--276.
Aka, Menny ; Einsiedler, Manfred ; Shapira, Uri . Integer points on spheres and their orthogonal lattices.
Invent. Math. 206 (2016), no. 2, 379--396.Sun, 27 Oct 2019 09:00:00 +0000Anonymous92997 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil?delta=0" >Kazhdan Sunday seminar: "Computation, quantumness, symplectic geometry, and information" (Gil Kalai, Leonid Polterovich, with participation of Dorit Aharonov and Guy Kindler)</a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil
Tentative syllabus
1. Mathematical models of classical and quantum mechanics.
2. Correspondence principle and quantization.
3. Classical and quantum computation: gates, circuits, algorithms
(Shor, Grover). Solovay-Kitaev. Some ideas of cryptography
4. Quantum noise and measurement, and rigidity of the Poisson bracket.
5. Noisy classical and quantum computing and error correction, threshold theorem- quantum fault tolerance (small noise is good for quantum computation). Kitaev's surface code.
6. Quantum speed limit/time-energy uncertainty vs symplectic displacement energy.
7. Time-energy uncertainty and quantum computation (Dorit or her student?)
8. Berezin transform, Markov chains, spectral gap, noise.
9. Adiabatic computation, quantum PCP (probabilistically checkable proofs) conjecture
[? under discussion]
10. Noise stability and noise sensitivity of Boolean functions, noisy boson
sampling
11. Connection to quantum field theory (Guy?).
Literature:
Aharonov, D. Quantum computation, In "Annual Reviews of Computational Physics" VI, 1999
(pp. 259-346).
<a href="https://arxiv.org/abs/quant-ph/9812037">https://arxiv.org/abs/quant-ph/9812037</a>
Kalai, G., Three puzzles on mathematics computations, and games, Proc. Int
Congress Math 2018, Rio de Janeiro, Vol. 1 pp. 551–606.
<a href="https://arxiv.org/abs/1801.02602">https://arxiv.org/abs/1801.02602</a>
Nielsen, M.A., and Chuang, I.L., Quantum computation and quantum information. Cambridge University Press, Cambridge, 2000.
Polterovich, L., Symplectic rigidity and quantum mechanics, European Congress of Mathematics, 155–179, Eur. Math. Soc., Zürich, 2018.
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rigidity-and-quantum-mechanics">https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rig...</a>
Polterovich L., and Rosen D., Function theory on symplectic manifolds. American Mathematical Society; 2014. [Chapters 1,9]
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/function-theory-on-symplectic-manifolds">https://sites.google.com/site/polterov/miscellaneoustexts/function-theor...</a>
Wigderson, A., Mathematics and computation, Princeton Univ. Press, 2019.
<a href="https://www.math.ias.edu/files/mathandcomp.pdf">https://www.math.ias.edu/files/mathandcomp.pdf</a>Sun, 27 Oct 2019 12:00:00 +0000Anonymous92999 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze?delta=0" >Kazhdan Sunday seminar: Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze) </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze
Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze)
Abstract: We shall discuss (Weil) cohomology theories for algebraic varieties.
When working with schemes over p-complete rings and taking cohomologies with p-complete coefficients one gets a plurality of such cohomology theories (e'tale, De-Rahm, Crystalline, etc.. ). The comparison between these different cohomology theories is a subtle subject known as "p-adic hodge theory" .
Recently Bhatt and Scholze defined a new such cohomology theory called prismatic cohomology. Remarkably, prismatic cohomology is easier to define than most p-adic cohomology theories and in the same specialized to each of them.The main new tool is the notions of delta-rings and prisms.
We shall start discussing general Weil) cohomology theories for algebraic varieties and give basic examples, we then move to develop the algebra of delta-rings and prisms, we then define the prisamtic site and prismatic cohomology. We shall then continue with comparison theorems and finally some applications Sun, 27 Oct 2019 14:00:00 +0000Anonymous92998 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows?delta=1" >Kazhdan Sunday seminar: Elon Lindenstrauss "Arithmetic applications of diagonal flows" </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows
Elon Lindenstrauss "Arithmetic applications of diagonal flows"
I will give an introduction to the dynamics of higher rank diagonal flows on homogeneous spaces,
including both the rigidity theorems of such flows and their applications to orbits of arithmetic interest,
in particular CM points and integer points on spheres.
I hope to cover parts of the following papers:
Einsiedler, Manfred ; Lindenstrauss, Elon ; Michel, Philippe ; Venkatesh, Akshay . The distribution of closed geodesics
on the modular surface, and Duke's theorem. Enseign. Math. (2) 58 (2012), no. 3-4, 249--313.
Einsiedler, M., Lindenstrauss, E., Symmetry of entropy in higher rank diagonalizable actions and measure classification.
arXiv e-prints arXiv:1803.07762.
Einsiedler, M. & Lindenstrauss, E. .Joinings of higher rank torus actions on homogeneous spaces. Publ.math.IHES (2019).
<a href="https://doi.org/10.1007/s10240-019-00103-y">https://doi.org/10.1007/s10240-019-00103-y</a>
Khayutin, Ilya . Joint equidistribution of CM points. Ann. of Math. (2) 189 (2019), no. 1, 145--276.
Aka, Menny ; Einsiedler, Manfred ; Shapira, Uri . Integer points on spheres and their orthogonal lattices.
Invent. Math. 206 (2016), no. 2, 379--396.Sun, 27 Oct 2019 09:00:00 +0000Anonymous92997 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil?delta=1" >Kazhdan Sunday seminar: "Computation, quantumness, symplectic geometry, and information" (Gil Kalai, Leonid Polterovich, with participation of Dorit Aharonov and Guy Kindler)</a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil
Tentative syllabus
1. Mathematical models of classical and quantum mechanics.
2. Correspondence principle and quantization.
3. Classical and quantum computation: gates, circuits, algorithms
(Shor, Grover). Solovay-Kitaev. Some ideas of cryptography
4. Quantum noise and measurement, and rigidity of the Poisson bracket.
5. Noisy classical and quantum computing and error correction, threshold theorem- quantum fault tolerance (small noise is good for quantum computation). Kitaev's surface code.
6. Quantum speed limit/time-energy uncertainty vs symplectic displacement energy.
7. Time-energy uncertainty and quantum computation (Dorit or her student?)
8. Berezin transform, Markov chains, spectral gap, noise.
9. Adiabatic computation, quantum PCP (probabilistically checkable proofs) conjecture
[? under discussion]
10. Noise stability and noise sensitivity of Boolean functions, noisy boson
sampling
11. Connection to quantum field theory (Guy?).
Literature:
Aharonov, D. Quantum computation, In "Annual Reviews of Computational Physics" VI, 1999
(pp. 259-346).
<a href="https://arxiv.org/abs/quant-ph/9812037">https://arxiv.org/abs/quant-ph/9812037</a>
Kalai, G., Three puzzles on mathematics computations, and games, Proc. Int
Congress Math 2018, Rio de Janeiro, Vol. 1 pp. 551–606.
<a href="https://arxiv.org/abs/1801.02602">https://arxiv.org/abs/1801.02602</a>
Nielsen, M.A., and Chuang, I.L., Quantum computation and quantum information. Cambridge University Press, Cambridge, 2000.
Polterovich, L., Symplectic rigidity and quantum mechanics, European Congress of Mathematics, 155–179, Eur. Math. Soc., Zürich, 2018.
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rigidity-and-quantum-mechanics">https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rig...</a>
Polterovich L., and Rosen D., Function theory on symplectic manifolds. American Mathematical Society; 2014. [Chapters 1,9]
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/function-theory-on-symplectic-manifolds">https://sites.google.com/site/polterov/miscellaneoustexts/function-theor...</a>
Wigderson, A., Mathematics and computation, Princeton Univ. Press, 2019.
<a href="https://www.math.ias.edu/files/mathandcomp.pdf">https://www.math.ias.edu/files/mathandcomp.pdf</a>Sun, 27 Oct 2019 12:00:00 +0000Anonymous92999 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze?delta=1" >Kazhdan Sunday seminar: Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze) </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze
Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze)
Abstract: We shall discuss (Weil) cohomology theories for algebraic varieties.
When working with schemes over p-complete rings and taking cohomologies with p-complete coefficients one gets a plurality of such cohomology theories (e'tale, De-Rahm, Crystalline, etc.. ). The comparison between these different cohomology theories is a subtle subject known as "p-adic hodge theory" .
Recently Bhatt and Scholze defined a new such cohomology theory called prismatic cohomology. Remarkably, prismatic cohomology is easier to define than most p-adic cohomology theories and in the same specialized to each of them.The main new tool is the notions of delta-rings and prisms.
We shall start discussing general Weil) cohomology theories for algebraic varieties and give basic examples, we then move to develop the algebra of delta-rings and prisms, we then define the prisamtic site and prismatic cohomology. We shall then continue with comparison theorems and finally some applications Sun, 27 Oct 2019 14:00:00 +0000Anonymous92998 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows?delta=2" >Kazhdan Sunday seminar: Elon Lindenstrauss "Arithmetic applications of diagonal flows" </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows
Elon Lindenstrauss "Arithmetic applications of diagonal flows"
I will give an introduction to the dynamics of higher rank diagonal flows on homogeneous spaces,
including both the rigidity theorems of such flows and their applications to orbits of arithmetic interest,
in particular CM points and integer points on spheres.
I hope to cover parts of the following papers:
Einsiedler, Manfred ; Lindenstrauss, Elon ; Michel, Philippe ; Venkatesh, Akshay . The distribution of closed geodesics
on the modular surface, and Duke's theorem. Enseign. Math. (2) 58 (2012), no. 3-4, 249--313.
Einsiedler, M., Lindenstrauss, E., Symmetry of entropy in higher rank diagonalizable actions and measure classification.
arXiv e-prints arXiv:1803.07762.
Einsiedler, M. & Lindenstrauss, E. .Joinings of higher rank torus actions on homogeneous spaces. Publ.math.IHES (2019).
<a href="https://doi.org/10.1007/s10240-019-00103-y">https://doi.org/10.1007/s10240-019-00103-y</a>
Khayutin, Ilya . Joint equidistribution of CM points. Ann. of Math. (2) 189 (2019), no. 1, 145--276.
Aka, Menny ; Einsiedler, Manfred ; Shapira, Uri . Integer points on spheres and their orthogonal lattices.
Invent. Math. 206 (2016), no. 2, 379--396.Sun, 27 Oct 2019 09:00:00 +0000Anonymous92997 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil?delta=2" >Kazhdan Sunday seminar: "Computation, quantumness, symplectic geometry, and information" (Gil Kalai, Leonid Polterovich, with participation of Dorit Aharonov and Guy Kindler)</a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil
Tentative syllabus
1. Mathematical models of classical and quantum mechanics.
2. Correspondence principle and quantization.
3. Classical and quantum computation: gates, circuits, algorithms
(Shor, Grover). Solovay-Kitaev. Some ideas of cryptography
4. Quantum noise and measurement, and rigidity of the Poisson bracket.
5. Noisy classical and quantum computing and error correction, threshold theorem- quantum fault tolerance (small noise is good for quantum computation). Kitaev's surface code.
6. Quantum speed limit/time-energy uncertainty vs symplectic displacement energy.
7. Time-energy uncertainty and quantum computation (Dorit or her student?)
8. Berezin transform, Markov chains, spectral gap, noise.
9. Adiabatic computation, quantum PCP (probabilistically checkable proofs) conjecture
[? under discussion]
10. Noise stability and noise sensitivity of Boolean functions, noisy boson
sampling
11. Connection to quantum field theory (Guy?).
Literature:
Aharonov, D. Quantum computation, In "Annual Reviews of Computational Physics" VI, 1999
(pp. 259-346).
<a href="https://arxiv.org/abs/quant-ph/9812037">https://arxiv.org/abs/quant-ph/9812037</a>
Kalai, G., Three puzzles on mathematics computations, and games, Proc. Int
Congress Math 2018, Rio de Janeiro, Vol. 1 pp. 551–606.
<a href="https://arxiv.org/abs/1801.02602">https://arxiv.org/abs/1801.02602</a>
Nielsen, M.A., and Chuang, I.L., Quantum computation and quantum information. Cambridge University Press, Cambridge, 2000.
Polterovich, L., Symplectic rigidity and quantum mechanics, European Congress of Mathematics, 155–179, Eur. Math. Soc., Zürich, 2018.
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rigidity-and-quantum-mechanics">https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rig...</a>
Polterovich L., and Rosen D., Function theory on symplectic manifolds. American Mathematical Society; 2014. [Chapters 1,9]
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/function-theory-on-symplectic-manifolds">https://sites.google.com/site/polterov/miscellaneoustexts/function-theor...</a>
Wigderson, A., Mathematics and computation, Princeton Univ. Press, 2019.
<a href="https://www.math.ias.edu/files/mathandcomp.pdf">https://www.math.ias.edu/files/mathandcomp.pdf</a>Sun, 27 Oct 2019 12:00:00 +0000Anonymous92999 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze?delta=2" >Kazhdan Sunday seminar: Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze) </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze
Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze)
Abstract: We shall discuss (Weil) cohomology theories for algebraic varieties.
When working with schemes over p-complete rings and taking cohomologies with p-complete coefficients one gets a plurality of such cohomology theories (e'tale, De-Rahm, Crystalline, etc.. ). The comparison between these different cohomology theories is a subtle subject known as "p-adic hodge theory" .
Recently Bhatt and Scholze defined a new such cohomology theory called prismatic cohomology. Remarkably, prismatic cohomology is easier to define than most p-adic cohomology theories and in the same specialized to each of them.The main new tool is the notions of delta-rings and prisms.
We shall start discussing general Weil) cohomology theories for algebraic varieties and give basic examples, we then move to develop the algebra of delta-rings and prisms, we then define the prisamtic site and prismatic cohomology. We shall then continue with comparison theorems and finally some applications Sun, 27 Oct 2019 14:00:00 +0000Anonymous92998 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows?delta=3" >Kazhdan Sunday seminar: Elon Lindenstrauss "Arithmetic applications of diagonal flows" </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows
Elon Lindenstrauss "Arithmetic applications of diagonal flows"
I will give an introduction to the dynamics of higher rank diagonal flows on homogeneous spaces,
including both the rigidity theorems of such flows and their applications to orbits of arithmetic interest,
in particular CM points and integer points on spheres.
I hope to cover parts of the following papers:
Einsiedler, Manfred ; Lindenstrauss, Elon ; Michel, Philippe ; Venkatesh, Akshay . The distribution of closed geodesics
on the modular surface, and Duke's theorem. Enseign. Math. (2) 58 (2012), no. 3-4, 249--313.
Einsiedler, M., Lindenstrauss, E., Symmetry of entropy in higher rank diagonalizable actions and measure classification.
arXiv e-prints arXiv:1803.07762.
Einsiedler, M. & Lindenstrauss, E. .Joinings of higher rank torus actions on homogeneous spaces. Publ.math.IHES (2019).
<a href="https://doi.org/10.1007/s10240-019-00103-y">https://doi.org/10.1007/s10240-019-00103-y</a>
Khayutin, Ilya . Joint equidistribution of CM points. Ann. of Math. (2) 189 (2019), no. 1, 145--276.
Aka, Menny ; Einsiedler, Manfred ; Shapira, Uri . Integer points on spheres and their orthogonal lattices.
Invent. Math. 206 (2016), no. 2, 379--396.Sun, 27 Oct 2019 09:00:00 +0000Anonymous92997 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil?delta=3" >Kazhdan Sunday seminar: "Computation, quantumness, symplectic geometry, and information" (Gil Kalai, Leonid Polterovich, with participation of Dorit Aharonov and Guy Kindler)</a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil
Tentative syllabus
1. Mathematical models of classical and quantum mechanics.
2. Correspondence principle and quantization.
3. Classical and quantum computation: gates, circuits, algorithms
(Shor, Grover). Solovay-Kitaev. Some ideas of cryptography
4. Quantum noise and measurement, and rigidity of the Poisson bracket.
5. Noisy classical and quantum computing and error correction, threshold theorem- quantum fault tolerance (small noise is good for quantum computation). Kitaev's surface code.
6. Quantum speed limit/time-energy uncertainty vs symplectic displacement energy.
7. Time-energy uncertainty and quantum computation (Dorit or her student?)
8. Berezin transform, Markov chains, spectral gap, noise.
9. Adiabatic computation, quantum PCP (probabilistically checkable proofs) conjecture
[? under discussion]
10. Noise stability and noise sensitivity of Boolean functions, noisy boson
sampling
11. Connection to quantum field theory (Guy?).
Literature:
Aharonov, D. Quantum computation, In "Annual Reviews of Computational Physics" VI, 1999
(pp. 259-346).
<a href="https://arxiv.org/abs/quant-ph/9812037">https://arxiv.org/abs/quant-ph/9812037</a>
Kalai, G., Three puzzles on mathematics computations, and games, Proc. Int
Congress Math 2018, Rio de Janeiro, Vol. 1 pp. 551–606.
<a href="https://arxiv.org/abs/1801.02602">https://arxiv.org/abs/1801.02602</a>
Nielsen, M.A., and Chuang, I.L., Quantum computation and quantum information. Cambridge University Press, Cambridge, 2000.
Polterovich, L., Symplectic rigidity and quantum mechanics, European Congress of Mathematics, 155–179, Eur. Math. Soc., Zürich, 2018.
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rigidity-and-quantum-mechanics">https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rig...</a>
Polterovich L., and Rosen D., Function theory on symplectic manifolds. American Mathematical Society; 2014. [Chapters 1,9]
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/function-theory-on-symplectic-manifolds">https://sites.google.com/site/polterov/miscellaneoustexts/function-theor...</a>
Wigderson, A., Mathematics and computation, Princeton Univ. Press, 2019.
<a href="https://www.math.ias.edu/files/mathandcomp.pdf">https://www.math.ias.edu/files/mathandcomp.pdf</a>Sun, 27 Oct 2019 12:00:00 +0000Anonymous92999 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze?delta=3" >Kazhdan Sunday seminar: Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze) </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze
Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze)
Abstract: We shall discuss (Weil) cohomology theories for algebraic varieties.
When working with schemes over p-complete rings and taking cohomologies with p-complete coefficients one gets a plurality of such cohomology theories (e'tale, De-Rahm, Crystalline, etc.. ). The comparison between these different cohomology theories is a subtle subject known as "p-adic hodge theory" .
Recently Bhatt and Scholze defined a new such cohomology theory called prismatic cohomology. Remarkably, prismatic cohomology is easier to define than most p-adic cohomology theories and in the same specialized to each of them.The main new tool is the notions of delta-rings and prisms.
We shall start discussing general Weil) cohomology theories for algebraic varieties and give basic examples, we then move to develop the algebra of delta-rings and prisms, we then define the prisamtic site and prismatic cohomology. We shall then continue with comparison theorems and finally some applications Sun, 27 Oct 2019 14:00:00 +0000Anonymous92998 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows?delta=4" >Kazhdan Sunday seminar: Elon Lindenstrauss "Arithmetic applications of diagonal flows" </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows
Elon Lindenstrauss "Arithmetic applications of diagonal flows"
I will give an introduction to the dynamics of higher rank diagonal flows on homogeneous spaces,
including both the rigidity theorems of such flows and their applications to orbits of arithmetic interest,
in particular CM points and integer points on spheres.
I hope to cover parts of the following papers:
Einsiedler, Manfred ; Lindenstrauss, Elon ; Michel, Philippe ; Venkatesh, Akshay . The distribution of closed geodesics
on the modular surface, and Duke's theorem. Enseign. Math. (2) 58 (2012), no. 3-4, 249--313.
Einsiedler, M., Lindenstrauss, E., Symmetry of entropy in higher rank diagonalizable actions and measure classification.
arXiv e-prints arXiv:1803.07762.
Einsiedler, M. & Lindenstrauss, E. .Joinings of higher rank torus actions on homogeneous spaces. Publ.math.IHES (2019).
<a href="https://doi.org/10.1007/s10240-019-00103-y">https://doi.org/10.1007/s10240-019-00103-y</a>
Khayutin, Ilya . Joint equidistribution of CM points. Ann. of Math. (2) 189 (2019), no. 1, 145--276.
Aka, Menny ; Einsiedler, Manfred ; Shapira, Uri . Integer points on spheres and their orthogonal lattices.
Invent. Math. 206 (2016), no. 2, 379--396.Sun, 27 Oct 2019 09:00:00 +0000Anonymous92997 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil?delta=4" >Kazhdan Sunday seminar: "Computation, quantumness, symplectic geometry, and information" (Gil Kalai, Leonid Polterovich, with participation of Dorit Aharonov and Guy Kindler)</a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil
Tentative syllabus
1. Mathematical models of classical and quantum mechanics.
2. Correspondence principle and quantization.
3. Classical and quantum computation: gates, circuits, algorithms
(Shor, Grover). Solovay-Kitaev. Some ideas of cryptography
4. Quantum noise and measurement, and rigidity of the Poisson bracket.
5. Noisy classical and quantum computing and error correction, threshold theorem- quantum fault tolerance (small noise is good for quantum computation). Kitaev's surface code.
6. Quantum speed limit/time-energy uncertainty vs symplectic displacement energy.
7. Time-energy uncertainty and quantum computation (Dorit or her student?)
8. Berezin transform, Markov chains, spectral gap, noise.
9. Adiabatic computation, quantum PCP (probabilistically checkable proofs) conjecture
[? under discussion]
10. Noise stability and noise sensitivity of Boolean functions, noisy boson
sampling
11. Connection to quantum field theory (Guy?).
Literature:
Aharonov, D. Quantum computation, In "Annual Reviews of Computational Physics" VI, 1999
(pp. 259-346).
<a href="https://arxiv.org/abs/quant-ph/9812037">https://arxiv.org/abs/quant-ph/9812037</a>
Kalai, G., Three puzzles on mathematics computations, and games, Proc. Int
Congress Math 2018, Rio de Janeiro, Vol. 1 pp. 551–606.
<a href="https://arxiv.org/abs/1801.02602">https://arxiv.org/abs/1801.02602</a>
Nielsen, M.A., and Chuang, I.L., Quantum computation and quantum information. Cambridge University Press, Cambridge, 2000.
Polterovich, L., Symplectic rigidity and quantum mechanics, European Congress of Mathematics, 155–179, Eur. Math. Soc., Zürich, 2018.
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rigidity-and-quantum-mechanics">https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rig...</a>
Polterovich L., and Rosen D., Function theory on symplectic manifolds. American Mathematical Society; 2014. [Chapters 1,9]
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/function-theory-on-symplectic-manifolds">https://sites.google.com/site/polterov/miscellaneoustexts/function-theor...</a>
Wigderson, A., Mathematics and computation, Princeton Univ. Press, 2019.
<a href="https://www.math.ias.edu/files/mathandcomp.pdf">https://www.math.ias.edu/files/mathandcomp.pdf</a>Sun, 27 Oct 2019 12:00:00 +0000Anonymous92999 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze?delta=4" >Kazhdan Sunday seminar: Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze) </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze
Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze)
Abstract: We shall discuss (Weil) cohomology theories for algebraic varieties.
When working with schemes over p-complete rings and taking cohomologies with p-complete coefficients one gets a plurality of such cohomology theories (e'tale, De-Rahm, Crystalline, etc.. ). The comparison between these different cohomology theories is a subtle subject known as "p-adic hodge theory" .
Recently Bhatt and Scholze defined a new such cohomology theory called prismatic cohomology. Remarkably, prismatic cohomology is easier to define than most p-adic cohomology theories and in the same specialized to each of them.The main new tool is the notions of delta-rings and prisms.
We shall start discussing general Weil) cohomology theories for algebraic varieties and give basic examples, we then move to develop the algebra of delta-rings and prisms, we then define the prisamtic site and prismatic cohomology. We shall then continue with comparison theorems and finally some applications Sun, 27 Oct 2019 14:00:00 +0000Anonymous92998 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows?delta=5" >Kazhdan Sunday seminar: Elon Lindenstrauss "Arithmetic applications of diagonal flows" </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows
Elon Lindenstrauss "Arithmetic applications of diagonal flows"
I will give an introduction to the dynamics of higher rank diagonal flows on homogeneous spaces,
including both the rigidity theorems of such flows and their applications to orbits of arithmetic interest,
in particular CM points and integer points on spheres.
I hope to cover parts of the following papers:
Einsiedler, Manfred ; Lindenstrauss, Elon ; Michel, Philippe ; Venkatesh, Akshay . The distribution of closed geodesics
on the modular surface, and Duke's theorem. Enseign. Math. (2) 58 (2012), no. 3-4, 249--313.
Einsiedler, M., Lindenstrauss, E., Symmetry of entropy in higher rank diagonalizable actions and measure classification.
arXiv e-prints arXiv:1803.07762.
Einsiedler, M. & Lindenstrauss, E. .Joinings of higher rank torus actions on homogeneous spaces. Publ.math.IHES (2019).
<a href="https://doi.org/10.1007/s10240-019-00103-y">https://doi.org/10.1007/s10240-019-00103-y</a>
Khayutin, Ilya . Joint equidistribution of CM points. Ann. of Math. (2) 189 (2019), no. 1, 145--276.
Aka, Menny ; Einsiedler, Manfred ; Shapira, Uri . Integer points on spheres and their orthogonal lattices.
Invent. Math. 206 (2016), no. 2, 379--396.Sun, 27 Oct 2019 09:00:00 +0000Anonymous92997 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil?delta=5" >Kazhdan Sunday seminar: "Computation, quantumness, symplectic geometry, and information" (Gil Kalai, Leonid Polterovich, with participation of Dorit Aharonov and Guy Kindler)</a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil
Tentative syllabus
1. Mathematical models of classical and quantum mechanics.
2. Correspondence principle and quantization.
3. Classical and quantum computation: gates, circuits, algorithms
(Shor, Grover). Solovay-Kitaev. Some ideas of cryptography
4. Quantum noise and measurement, and rigidity of the Poisson bracket.
5. Noisy classical and quantum computing and error correction, threshold theorem- quantum fault tolerance (small noise is good for quantum computation). Kitaev's surface code.
6. Quantum speed limit/time-energy uncertainty vs symplectic displacement energy.
7. Time-energy uncertainty and quantum computation (Dorit or her student?)
8. Berezin transform, Markov chains, spectral gap, noise.
9. Adiabatic computation, quantum PCP (probabilistically checkable proofs) conjecture
[? under discussion]
10. Noise stability and noise sensitivity of Boolean functions, noisy boson
sampling
11. Connection to quantum field theory (Guy?).
Literature:
Aharonov, D. Quantum computation, In "Annual Reviews of Computational Physics" VI, 1999
(pp. 259-346).
<a href="https://arxiv.org/abs/quant-ph/9812037">https://arxiv.org/abs/quant-ph/9812037</a>
Kalai, G., Three puzzles on mathematics computations, and games, Proc. Int
Congress Math 2018, Rio de Janeiro, Vol. 1 pp. 551–606.
<a href="https://arxiv.org/abs/1801.02602">https://arxiv.org/abs/1801.02602</a>
Nielsen, M.A., and Chuang, I.L., Quantum computation and quantum information. Cambridge University Press, Cambridge, 2000.
Polterovich, L., Symplectic rigidity and quantum mechanics, European Congress of Mathematics, 155–179, Eur. Math. Soc., Zürich, 2018.
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rigidity-and-quantum-mechanics">https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rig...</a>
Polterovich L., and Rosen D., Function theory on symplectic manifolds. American Mathematical Society; 2014. [Chapters 1,9]
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/function-theory-on-symplectic-manifolds">https://sites.google.com/site/polterov/miscellaneoustexts/function-theor...</a>
Wigderson, A., Mathematics and computation, Princeton Univ. Press, 2019.
<a href="https://www.math.ias.edu/files/mathandcomp.pdf">https://www.math.ias.edu/files/mathandcomp.pdf</a>Sun, 27 Oct 2019 12:00:00 +0000Anonymous92999 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze?delta=5" >Kazhdan Sunday seminar: Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze) </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze
Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze)
Abstract: We shall discuss (Weil) cohomology theories for algebraic varieties.
When working with schemes over p-complete rings and taking cohomologies with p-complete coefficients one gets a plurality of such cohomology theories (e'tale, De-Rahm, Crystalline, etc.. ). The comparison between these different cohomology theories is a subtle subject known as "p-adic hodge theory" .
Recently Bhatt and Scholze defined a new such cohomology theory called prismatic cohomology. Remarkably, prismatic cohomology is easier to define than most p-adic cohomology theories and in the same specialized to each of them.The main new tool is the notions of delta-rings and prisms.
We shall start discussing general Weil) cohomology theories for algebraic varieties and give basic examples, we then move to develop the algebra of delta-rings and prisms, we then define the prisamtic site and prismatic cohomology. We shall then continue with comparison theorems and finally some applications Sun, 27 Oct 2019 14:00:00 +0000Anonymous92998 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows?delta=6" >Kazhdan Sunday seminar: Elon Lindenstrauss "Arithmetic applications of diagonal flows" </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows
Elon Lindenstrauss "Arithmetic applications of diagonal flows"
I will give an introduction to the dynamics of higher rank diagonal flows on homogeneous spaces,
including both the rigidity theorems of such flows and their applications to orbits of arithmetic interest,
in particular CM points and integer points on spheres.
I hope to cover parts of the following papers:
Einsiedler, Manfred ; Lindenstrauss, Elon ; Michel, Philippe ; Venkatesh, Akshay . The distribution of closed geodesics
on the modular surface, and Duke's theorem. Enseign. Math. (2) 58 (2012), no. 3-4, 249--313.
Einsiedler, M., Lindenstrauss, E., Symmetry of entropy in higher rank diagonalizable actions and measure classification.
arXiv e-prints arXiv:1803.07762.
Einsiedler, M. & Lindenstrauss, E. .Joinings of higher rank torus actions on homogeneous spaces. Publ.math.IHES (2019).
<a href="https://doi.org/10.1007/s10240-019-00103-y">https://doi.org/10.1007/s10240-019-00103-y</a>
Khayutin, Ilya . Joint equidistribution of CM points. Ann. of Math. (2) 189 (2019), no. 1, 145--276.
Aka, Menny ; Einsiedler, Manfred ; Shapira, Uri . Integer points on spheres and their orthogonal lattices.
Invent. Math. 206 (2016), no. 2, 379--396.Sun, 27 Oct 2019 09:00:00 +0000Anonymous92997 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil?delta=6" >Kazhdan Sunday seminar: "Computation, quantumness, symplectic geometry, and information" (Gil Kalai, Leonid Polterovich, with participation of Dorit Aharonov and Guy Kindler)</a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil
Tentative syllabus
1. Mathematical models of classical and quantum mechanics.
2. Correspondence principle and quantization.
3. Classical and quantum computation: gates, circuits, algorithms
(Shor, Grover). Solovay-Kitaev. Some ideas of cryptography
4. Quantum noise and measurement, and rigidity of the Poisson bracket.
5. Noisy classical and quantum computing and error correction, threshold theorem- quantum fault tolerance (small noise is good for quantum computation). Kitaev's surface code.
6. Quantum speed limit/time-energy uncertainty vs symplectic displacement energy.
7. Time-energy uncertainty and quantum computation (Dorit or her student?)
8. Berezin transform, Markov chains, spectral gap, noise.
9. Adiabatic computation, quantum PCP (probabilistically checkable proofs) conjecture
[? under discussion]
10. Noise stability and noise sensitivity of Boolean functions, noisy boson
sampling
11. Connection to quantum field theory (Guy?).
Literature:
Aharonov, D. Quantum computation, In "Annual Reviews of Computational Physics" VI, 1999
(pp. 259-346).
<a href="https://arxiv.org/abs/quant-ph/9812037">https://arxiv.org/abs/quant-ph/9812037</a>
Kalai, G., Three puzzles on mathematics computations, and games, Proc. Int
Congress Math 2018, Rio de Janeiro, Vol. 1 pp. 551–606.
<a href="https://arxiv.org/abs/1801.02602">https://arxiv.org/abs/1801.02602</a>
Nielsen, M.A., and Chuang, I.L., Quantum computation and quantum information. Cambridge University Press, Cambridge, 2000.
Polterovich, L., Symplectic rigidity and quantum mechanics, European Congress of Mathematics, 155–179, Eur. Math. Soc., Zürich, 2018.
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rigidity-and-quantum-mechanics">https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rig...</a>
Polterovich L., and Rosen D., Function theory on symplectic manifolds. American Mathematical Society; 2014. [Chapters 1,9]
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/function-theory-on-symplectic-manifolds">https://sites.google.com/site/polterov/miscellaneoustexts/function-theor...</a>
Wigderson, A., Mathematics and computation, Princeton Univ. Press, 2019.
<a href="https://www.math.ias.edu/files/mathandcomp.pdf">https://www.math.ias.edu/files/mathandcomp.pdf</a>Sun, 27 Oct 2019 12:00:00 +0000Anonymous92999 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze?delta=6" >Kazhdan Sunday seminar: Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze) </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze
Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze)
Abstract: We shall discuss (Weil) cohomology theories for algebraic varieties.
When working with schemes over p-complete rings and taking cohomologies with p-complete coefficients one gets a plurality of such cohomology theories (e'tale, De-Rahm, Crystalline, etc.. ). The comparison between these different cohomology theories is a subtle subject known as "p-adic hodge theory" .
Recently Bhatt and Scholze defined a new such cohomology theory called prismatic cohomology. Remarkably, prismatic cohomology is easier to define than most p-adic cohomology theories and in the same specialized to each of them.The main new tool is the notions of delta-rings and prisms.
We shall start discussing general Weil) cohomology theories for algebraic varieties and give basic examples, we then move to develop the algebra of delta-rings and prisms, we then define the prisamtic site and prismatic cohomology. We shall then continue with comparison theorems and finally some applications Sun, 27 Oct 2019 14:00:00 +0000Anonymous92998 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows?delta=7" >Kazhdan Sunday seminar: Elon Lindenstrauss "Arithmetic applications of diagonal flows" </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows
Elon Lindenstrauss "Arithmetic applications of diagonal flows"
I will give an introduction to the dynamics of higher rank diagonal flows on homogeneous spaces,
including both the rigidity theorems of such flows and their applications to orbits of arithmetic interest,
in particular CM points and integer points on spheres.
I hope to cover parts of the following papers:
Einsiedler, Manfred ; Lindenstrauss, Elon ; Michel, Philippe ; Venkatesh, Akshay . The distribution of closed geodesics
on the modular surface, and Duke's theorem. Enseign. Math. (2) 58 (2012), no. 3-4, 249--313.
Einsiedler, M., Lindenstrauss, E., Symmetry of entropy in higher rank diagonalizable actions and measure classification.
arXiv e-prints arXiv:1803.07762.
Einsiedler, M. & Lindenstrauss, E. .Joinings of higher rank torus actions on homogeneous spaces. Publ.math.IHES (2019).
<a href="https://doi.org/10.1007/s10240-019-00103-y">https://doi.org/10.1007/s10240-019-00103-y</a>
Khayutin, Ilya . Joint equidistribution of CM points. Ann. of Math. (2) 189 (2019), no. 1, 145--276.
Aka, Menny ; Einsiedler, Manfred ; Shapira, Uri . Integer points on spheres and their orthogonal lattices.
Invent. Math. 206 (2016), no. 2, 379--396.Sun, 27 Oct 2019 09:00:00 +0000Anonymous92997 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil?delta=7" >Kazhdan Sunday seminar: "Computation, quantumness, symplectic geometry, and information" (Gil Kalai, Leonid Polterovich, with participation of Dorit Aharonov and Guy Kindler)</a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil
Tentative syllabus
1. Mathematical models of classical and quantum mechanics.
2. Correspondence principle and quantization.
3. Classical and quantum computation: gates, circuits, algorithms
(Shor, Grover). Solovay-Kitaev. Some ideas of cryptography
4. Quantum noise and measurement, and rigidity of the Poisson bracket.
5. Noisy classical and quantum computing and error correction, threshold theorem- quantum fault tolerance (small noise is good for quantum computation). Kitaev's surface code.
6. Quantum speed limit/time-energy uncertainty vs symplectic displacement energy.
7. Time-energy uncertainty and quantum computation (Dorit or her student?)
8. Berezin transform, Markov chains, spectral gap, noise.
9. Adiabatic computation, quantum PCP (probabilistically checkable proofs) conjecture
[? under discussion]
10. Noise stability and noise sensitivity of Boolean functions, noisy boson
sampling
11. Connection to quantum field theory (Guy?).
Literature:
Aharonov, D. Quantum computation, In "Annual Reviews of Computational Physics" VI, 1999
(pp. 259-346).
<a href="https://arxiv.org/abs/quant-ph/9812037">https://arxiv.org/abs/quant-ph/9812037</a>
Kalai, G., Three puzzles on mathematics computations, and games, Proc. Int
Congress Math 2018, Rio de Janeiro, Vol. 1 pp. 551–606.
<a href="https://arxiv.org/abs/1801.02602">https://arxiv.org/abs/1801.02602</a>
Nielsen, M.A., and Chuang, I.L., Quantum computation and quantum information. Cambridge University Press, Cambridge, 2000.
Polterovich, L., Symplectic rigidity and quantum mechanics, European Congress of Mathematics, 155–179, Eur. Math. Soc., Zürich, 2018.
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rigidity-and-quantum-mechanics">https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rig...</a>
Polterovich L., and Rosen D., Function theory on symplectic manifolds. American Mathematical Society; 2014. [Chapters 1,9]
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/function-theory-on-symplectic-manifolds">https://sites.google.com/site/polterov/miscellaneoustexts/function-theor...</a>
Wigderson, A., Mathematics and computation, Princeton Univ. Press, 2019.
<a href="https://www.math.ias.edu/files/mathandcomp.pdf">https://www.math.ias.edu/files/mathandcomp.pdf</a>Sun, 27 Oct 2019 12:00:00 +0000Anonymous92999 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze?delta=7" >Kazhdan Sunday seminar: Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze) </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze
Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze)
Abstract: We shall discuss (Weil) cohomology theories for algebraic varieties.
When working with schemes over p-complete rings and taking cohomologies with p-complete coefficients one gets a plurality of such cohomology theories (e'tale, De-Rahm, Crystalline, etc.. ). The comparison between these different cohomology theories is a subtle subject known as "p-adic hodge theory" .
Recently Bhatt and Scholze defined a new such cohomology theory called prismatic cohomology. Remarkably, prismatic cohomology is easier to define than most p-adic cohomology theories and in the same specialized to each of them.The main new tool is the notions of delta-rings and prisms.
We shall start discussing general Weil) cohomology theories for algebraic varieties and give basic examples, we then move to develop the algebra of delta-rings and prisms, we then define the prisamtic site and prismatic cohomology. We shall then continue with comparison theorems and finally some applications Sun, 27 Oct 2019 14:00:00 +0000Anonymous92998 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows?delta=8" >Kazhdan Sunday seminar: Elon Lindenstrauss "Arithmetic applications of diagonal flows" </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows
Elon Lindenstrauss "Arithmetic applications of diagonal flows"
I will give an introduction to the dynamics of higher rank diagonal flows on homogeneous spaces,
including both the rigidity theorems of such flows and their applications to orbits of arithmetic interest,
in particular CM points and integer points on spheres.
I hope to cover parts of the following papers:
Einsiedler, Manfred ; Lindenstrauss, Elon ; Michel, Philippe ; Venkatesh, Akshay . The distribution of closed geodesics
on the modular surface, and Duke's theorem. Enseign. Math. (2) 58 (2012), no. 3-4, 249--313.
Einsiedler, M., Lindenstrauss, E., Symmetry of entropy in higher rank diagonalizable actions and measure classification.
arXiv e-prints arXiv:1803.07762.
Einsiedler, M. & Lindenstrauss, E. .Joinings of higher rank torus actions on homogeneous spaces. Publ.math.IHES (2019).
<a href="https://doi.org/10.1007/s10240-019-00103-y">https://doi.org/10.1007/s10240-019-00103-y</a>
Khayutin, Ilya . Joint equidistribution of CM points. Ann. of Math. (2) 189 (2019), no. 1, 145--276.
Aka, Menny ; Einsiedler, Manfred ; Shapira, Uri . Integer points on spheres and their orthogonal lattices.
Invent. Math. 206 (2016), no. 2, 379--396.Sun, 27 Oct 2019 09:00:00 +0000Anonymous92997 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil?delta=8" >Kazhdan Sunday seminar: "Computation, quantumness, symplectic geometry, and information" (Gil Kalai, Leonid Polterovich, with participation of Dorit Aharonov and Guy Kindler)</a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil
Tentative syllabus
1. Mathematical models of classical and quantum mechanics.
2. Correspondence principle and quantization.
3. Classical and quantum computation: gates, circuits, algorithms
(Shor, Grover). Solovay-Kitaev. Some ideas of cryptography
4. Quantum noise and measurement, and rigidity of the Poisson bracket.
5. Noisy classical and quantum computing and error correction, threshold theorem- quantum fault tolerance (small noise is good for quantum computation). Kitaev's surface code.
6. Quantum speed limit/time-energy uncertainty vs symplectic displacement energy.
7. Time-energy uncertainty and quantum computation (Dorit or her student?)
8. Berezin transform, Markov chains, spectral gap, noise.
9. Adiabatic computation, quantum PCP (probabilistically checkable proofs) conjecture
[? under discussion]
10. Noise stability and noise sensitivity of Boolean functions, noisy boson
sampling
11. Connection to quantum field theory (Guy?).
Literature:
Aharonov, D. Quantum computation, In "Annual Reviews of Computational Physics" VI, 1999
(pp. 259-346).
<a href="https://arxiv.org/abs/quant-ph/9812037">https://arxiv.org/abs/quant-ph/9812037</a>
Kalai, G., Three puzzles on mathematics computations, and games, Proc. Int
Congress Math 2018, Rio de Janeiro, Vol. 1 pp. 551–606.
<a href="https://arxiv.org/abs/1801.02602">https://arxiv.org/abs/1801.02602</a>
Nielsen, M.A., and Chuang, I.L., Quantum computation and quantum information. Cambridge University Press, Cambridge, 2000.
Polterovich, L., Symplectic rigidity and quantum mechanics, European Congress of Mathematics, 155–179, Eur. Math. Soc., Zürich, 2018.
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rigidity-and-quantum-mechanics">https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rig...</a>
Polterovich L., and Rosen D., Function theory on symplectic manifolds. American Mathematical Society; 2014. [Chapters 1,9]
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/function-theory-on-symplectic-manifolds">https://sites.google.com/site/polterov/miscellaneoustexts/function-theor...</a>
Wigderson, A., Mathematics and computation, Princeton Univ. Press, 2019.
<a href="https://www.math.ias.edu/files/mathandcomp.pdf">https://www.math.ias.edu/files/mathandcomp.pdf</a>Sun, 27 Oct 2019 12:00:00 +0000Anonymous92999 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze?delta=8" >Kazhdan Sunday seminar: Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze) </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze
Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze)
Abstract: We shall discuss (Weil) cohomology theories for algebraic varieties.
When working with schemes over p-complete rings and taking cohomologies with p-complete coefficients one gets a plurality of such cohomology theories (e'tale, De-Rahm, Crystalline, etc.. ). The comparison between these different cohomology theories is a subtle subject known as "p-adic hodge theory" .
Recently Bhatt and Scholze defined a new such cohomology theory called prismatic cohomology. Remarkably, prismatic cohomology is easier to define than most p-adic cohomology theories and in the same specialized to each of them.The main new tool is the notions of delta-rings and prisms.
We shall start discussing general Weil) cohomology theories for algebraic varieties and give basic examples, we then move to develop the algebra of delta-rings and prisms, we then define the prisamtic site and prismatic cohomology. We shall then continue with comparison theorems and finally some applications Sun, 27 Oct 2019 14:00:00 +0000Anonymous92998 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows?delta=9" >Kazhdan Sunday seminar: Elon Lindenstrauss "Arithmetic applications of diagonal flows" </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows
Elon Lindenstrauss "Arithmetic applications of diagonal flows"
I will give an introduction to the dynamics of higher rank diagonal flows on homogeneous spaces,
including both the rigidity theorems of such flows and their applications to orbits of arithmetic interest,
in particular CM points and integer points on spheres.
I hope to cover parts of the following papers:
Einsiedler, Manfred ; Lindenstrauss, Elon ; Michel, Philippe ; Venkatesh, Akshay . The distribution of closed geodesics
on the modular surface, and Duke's theorem. Enseign. Math. (2) 58 (2012), no. 3-4, 249--313.
Einsiedler, M., Lindenstrauss, E., Symmetry of entropy in higher rank diagonalizable actions and measure classification.
arXiv e-prints arXiv:1803.07762.
Einsiedler, M. & Lindenstrauss, E. .Joinings of higher rank torus actions on homogeneous spaces. Publ.math.IHES (2019).
<a href="https://doi.org/10.1007/s10240-019-00103-y">https://doi.org/10.1007/s10240-019-00103-y</a>
Khayutin, Ilya . Joint equidistribution of CM points. Ann. of Math. (2) 189 (2019), no. 1, 145--276.
Aka, Menny ; Einsiedler, Manfred ; Shapira, Uri . Integer points on spheres and their orthogonal lattices.
Invent. Math. 206 (2016), no. 2, 379--396.Sun, 27 Oct 2019 09:00:00 +0000Anonymous92997 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil?delta=9" >Kazhdan Sunday seminar: "Computation, quantumness, symplectic geometry, and information" (Gil Kalai, Leonid Polterovich, with participation of Dorit Aharonov and Guy Kindler)</a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil
Tentative syllabus
1. Mathematical models of classical and quantum mechanics.
2. Correspondence principle and quantization.
3. Classical and quantum computation: gates, circuits, algorithms
(Shor, Grover). Solovay-Kitaev. Some ideas of cryptography
4. Quantum noise and measurement, and rigidity of the Poisson bracket.
5. Noisy classical and quantum computing and error correction, threshold theorem- quantum fault tolerance (small noise is good for quantum computation). Kitaev's surface code.
6. Quantum speed limit/time-energy uncertainty vs symplectic displacement energy.
7. Time-energy uncertainty and quantum computation (Dorit or her student?)
8. Berezin transform, Markov chains, spectral gap, noise.
9. Adiabatic computation, quantum PCP (probabilistically checkable proofs) conjecture
[? under discussion]
10. Noise stability and noise sensitivity of Boolean functions, noisy boson
sampling
11. Connection to quantum field theory (Guy?).
Literature:
Aharonov, D. Quantum computation, In "Annual Reviews of Computational Physics" VI, 1999
(pp. 259-346).
<a href="https://arxiv.org/abs/quant-ph/9812037">https://arxiv.org/abs/quant-ph/9812037</a>
Kalai, G., Three puzzles on mathematics computations, and games, Proc. Int
Congress Math 2018, Rio de Janeiro, Vol. 1 pp. 551–606.
<a href="https://arxiv.org/abs/1801.02602">https://arxiv.org/abs/1801.02602</a>
Nielsen, M.A., and Chuang, I.L., Quantum computation and quantum information. Cambridge University Press, Cambridge, 2000.
Polterovich, L., Symplectic rigidity and quantum mechanics, European Congress of Mathematics, 155–179, Eur. Math. Soc., Zürich, 2018.
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rigidity-and-quantum-mechanics">https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rig...</a>
Polterovich L., and Rosen D., Function theory on symplectic manifolds. American Mathematical Society; 2014. [Chapters 1,9]
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/function-theory-on-symplectic-manifolds">https://sites.google.com/site/polterov/miscellaneoustexts/function-theor...</a>
Wigderson, A., Mathematics and computation, Princeton Univ. Press, 2019.
<a href="https://www.math.ias.edu/files/mathandcomp.pdf">https://www.math.ias.edu/files/mathandcomp.pdf</a>Sun, 27 Oct 2019 12:00:00 +0000Anonymous92999 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze?delta=9" >Kazhdan Sunday seminar: Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze) </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze
Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze)
Abstract: We shall discuss (Weil) cohomology theories for algebraic varieties.
When working with schemes over p-complete rings and taking cohomologies with p-complete coefficients one gets a plurality of such cohomology theories (e'tale, De-Rahm, Crystalline, etc.. ). The comparison between these different cohomology theories is a subtle subject known as "p-adic hodge theory" .
Recently Bhatt and Scholze defined a new such cohomology theory called prismatic cohomology. Remarkably, prismatic cohomology is easier to define than most p-adic cohomology theories and in the same specialized to each of them.The main new tool is the notions of delta-rings and prisms.
We shall start discussing general Weil) cohomology theories for algebraic varieties and give basic examples, we then move to develop the algebra of delta-rings and prisms, we then define the prisamtic site and prismatic cohomology. We shall then continue with comparison theorems and finally some applications Sun, 27 Oct 2019 14:00:00 +0000Anonymous92998 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows?delta=10" >Kazhdan Sunday seminar: Elon Lindenstrauss "Arithmetic applications of diagonal flows" </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows
Elon Lindenstrauss "Arithmetic applications of diagonal flows"
I will give an introduction to the dynamics of higher rank diagonal flows on homogeneous spaces,
including both the rigidity theorems of such flows and their applications to orbits of arithmetic interest,
in particular CM points and integer points on spheres.
I hope to cover parts of the following papers:
Einsiedler, Manfred ; Lindenstrauss, Elon ; Michel, Philippe ; Venkatesh, Akshay . The distribution of closed geodesics
on the modular surface, and Duke's theorem. Enseign. Math. (2) 58 (2012), no. 3-4, 249--313.
Einsiedler, M., Lindenstrauss, E., Symmetry of entropy in higher rank diagonalizable actions and measure classification.
arXiv e-prints arXiv:1803.07762.
Einsiedler, M. & Lindenstrauss, E. .Joinings of higher rank torus actions on homogeneous spaces. Publ.math.IHES (2019).
<a href="https://doi.org/10.1007/s10240-019-00103-y">https://doi.org/10.1007/s10240-019-00103-y</a>
Khayutin, Ilya . Joint equidistribution of CM points. Ann. of Math. (2) 189 (2019), no. 1, 145--276.
Aka, Menny ; Einsiedler, Manfred ; Shapira, Uri . Integer points on spheres and their orthogonal lattices.
Invent. Math. 206 (2016), no. 2, 379--396.Sun, 27 Oct 2019 09:00:00 +0000Anonymous92997 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil?delta=10" >Kazhdan Sunday seminar: "Computation, quantumness, symplectic geometry, and information" (Gil Kalai, Leonid Polterovich, with participation of Dorit Aharonov and Guy Kindler)</a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil
Tentative syllabus
1. Mathematical models of classical and quantum mechanics.
2. Correspondence principle and quantization.
3. Classical and quantum computation: gates, circuits, algorithms
(Shor, Grover). Solovay-Kitaev. Some ideas of cryptography
4. Quantum noise and measurement, and rigidity of the Poisson bracket.
5. Noisy classical and quantum computing and error correction, threshold theorem- quantum fault tolerance (small noise is good for quantum computation). Kitaev's surface code.
6. Quantum speed limit/time-energy uncertainty vs symplectic displacement energy.
7. Time-energy uncertainty and quantum computation (Dorit or her student?)
8. Berezin transform, Markov chains, spectral gap, noise.
9. Adiabatic computation, quantum PCP (probabilistically checkable proofs) conjecture
[? under discussion]
10. Noise stability and noise sensitivity of Boolean functions, noisy boson
sampling
11. Connection to quantum field theory (Guy?).
Literature:
Aharonov, D. Quantum computation, In "Annual Reviews of Computational Physics" VI, 1999
(pp. 259-346).
<a href="https://arxiv.org/abs/quant-ph/9812037">https://arxiv.org/abs/quant-ph/9812037</a>
Kalai, G., Three puzzles on mathematics computations, and games, Proc. Int
Congress Math 2018, Rio de Janeiro, Vol. 1 pp. 551–606.
<a href="https://arxiv.org/abs/1801.02602">https://arxiv.org/abs/1801.02602</a>
Nielsen, M.A., and Chuang, I.L., Quantum computation and quantum information. Cambridge University Press, Cambridge, 2000.
Polterovich, L., Symplectic rigidity and quantum mechanics, European Congress of Mathematics, 155–179, Eur. Math. Soc., Zürich, 2018.
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rigidity-and-quantum-mechanics">https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rig...</a>
Polterovich L., and Rosen D., Function theory on symplectic manifolds. American Mathematical Society; 2014. [Chapters 1,9]
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/function-theory-on-symplectic-manifolds">https://sites.google.com/site/polterov/miscellaneoustexts/function-theor...</a>
Wigderson, A., Mathematics and computation, Princeton Univ. Press, 2019.
<a href="https://www.math.ias.edu/files/mathandcomp.pdf">https://www.math.ias.edu/files/mathandcomp.pdf</a>Sun, 27 Oct 2019 12:00:00 +0000Anonymous92999 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze?delta=10" >Kazhdan Sunday seminar: Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze) </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze
Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze)
Abstract: We shall discuss (Weil) cohomology theories for algebraic varieties.
When working with schemes over p-complete rings and taking cohomologies with p-complete coefficients one gets a plurality of such cohomology theories (e'tale, De-Rahm, Crystalline, etc.. ). The comparison between these different cohomology theories is a subtle subject known as "p-adic hodge theory" .
Recently Bhatt and Scholze defined a new such cohomology theory called prismatic cohomology. Remarkably, prismatic cohomology is easier to define than most p-adic cohomology theories and in the same specialized to each of them.The main new tool is the notions of delta-rings and prisms.
We shall start discussing general Weil) cohomology theories for algebraic varieties and give basic examples, we then move to develop the algebra of delta-rings and prisms, we then define the prisamtic site and prismatic cohomology. We shall then continue with comparison theorems and finally some applications Sun, 27 Oct 2019 14:00:00 +0000Anonymous92998 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows?delta=11" >Kazhdan Sunday seminar: Elon Lindenstrauss "Arithmetic applications of diagonal flows" </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows
Elon Lindenstrauss "Arithmetic applications of diagonal flows"
I will give an introduction to the dynamics of higher rank diagonal flows on homogeneous spaces,
including both the rigidity theorems of such flows and their applications to orbits of arithmetic interest,
in particular CM points and integer points on spheres.
I hope to cover parts of the following papers:
Einsiedler, Manfred ; Lindenstrauss, Elon ; Michel, Philippe ; Venkatesh, Akshay . The distribution of closed geodesics
on the modular surface, and Duke's theorem. Enseign. Math. (2) 58 (2012), no. 3-4, 249--313.
Einsiedler, M., Lindenstrauss, E., Symmetry of entropy in higher rank diagonalizable actions and measure classification.
arXiv e-prints arXiv:1803.07762.
Einsiedler, M. & Lindenstrauss, E. .Joinings of higher rank torus actions on homogeneous spaces. Publ.math.IHES (2019).
<a href="https://doi.org/10.1007/s10240-019-00103-y">https://doi.org/10.1007/s10240-019-00103-y</a>
Khayutin, Ilya . Joint equidistribution of CM points. Ann. of Math. (2) 189 (2019), no. 1, 145--276.
Aka, Menny ; Einsiedler, Manfred ; Shapira, Uri . Integer points on spheres and their orthogonal lattices.
Invent. Math. 206 (2016), no. 2, 379--396.Sun, 27 Oct 2019 09:00:00 +0000Anonymous92997 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil?delta=11" >Kazhdan Sunday seminar: "Computation, quantumness, symplectic geometry, and information" (Gil Kalai, Leonid Polterovich, with participation of Dorit Aharonov and Guy Kindler)</a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil
Tentative syllabus
1. Mathematical models of classical and quantum mechanics.
2. Correspondence principle and quantization.
3. Classical and quantum computation: gates, circuits, algorithms
(Shor, Grover). Solovay-Kitaev. Some ideas of cryptography
4. Quantum noise and measurement, and rigidity of the Poisson bracket.
5. Noisy classical and quantum computing and error correction, threshold theorem- quantum fault tolerance (small noise is good for quantum computation). Kitaev's surface code.
6. Quantum speed limit/time-energy uncertainty vs symplectic displacement energy.
7. Time-energy uncertainty and quantum computation (Dorit or her student?)
8. Berezin transform, Markov chains, spectral gap, noise.
9. Adiabatic computation, quantum PCP (probabilistically checkable proofs) conjecture
[? under discussion]
10. Noise stability and noise sensitivity of Boolean functions, noisy boson
sampling
11. Connection to quantum field theory (Guy?).
Literature:
Aharonov, D. Quantum computation, In "Annual Reviews of Computational Physics" VI, 1999
(pp. 259-346).
<a href="https://arxiv.org/abs/quant-ph/9812037">https://arxiv.org/abs/quant-ph/9812037</a>
Kalai, G., Three puzzles on mathematics computations, and games, Proc. Int
Congress Math 2018, Rio de Janeiro, Vol. 1 pp. 551–606.
<a href="https://arxiv.org/abs/1801.02602">https://arxiv.org/abs/1801.02602</a>
Nielsen, M.A., and Chuang, I.L., Quantum computation and quantum information. Cambridge University Press, Cambridge, 2000.
Polterovich, L., Symplectic rigidity and quantum mechanics, European Congress of Mathematics, 155–179, Eur. Math. Soc., Zürich, 2018.
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rigidity-and-quantum-mechanics">https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rig...</a>
Polterovich L., and Rosen D., Function theory on symplectic manifolds. American Mathematical Society; 2014. [Chapters 1,9]
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/function-theory-on-symplectic-manifolds">https://sites.google.com/site/polterov/miscellaneoustexts/function-theor...</a>
Wigderson, A., Mathematics and computation, Princeton Univ. Press, 2019.
<a href="https://www.math.ias.edu/files/mathandcomp.pdf">https://www.math.ias.edu/files/mathandcomp.pdf</a>Sun, 27 Oct 2019 12:00:00 +0000Anonymous92999 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze?delta=11" >Kazhdan Sunday seminar: Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze) </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze
Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze)
Abstract: We shall discuss (Weil) cohomology theories for algebraic varieties.
When working with schemes over p-complete rings and taking cohomologies with p-complete coefficients one gets a plurality of such cohomology theories (e'tale, De-Rahm, Crystalline, etc.. ). The comparison between these different cohomology theories is a subtle subject known as "p-adic hodge theory" .
Recently Bhatt and Scholze defined a new such cohomology theory called prismatic cohomology. Remarkably, prismatic cohomology is easier to define than most p-adic cohomology theories and in the same specialized to each of them.The main new tool is the notions of delta-rings and prisms.
We shall start discussing general Weil) cohomology theories for algebraic varieties and give basic examples, we then move to develop the algebra of delta-rings and prisms, we then define the prisamtic site and prismatic cohomology. We shall then continue with comparison theorems and finally some applications Sun, 27 Oct 2019 14:00:00 +0000Anonymous92998 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows?delta=12" >Kazhdan Sunday seminar: Elon Lindenstrauss "Arithmetic applications of diagonal flows" </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows
Elon Lindenstrauss "Arithmetic applications of diagonal flows"
I will give an introduction to the dynamics of higher rank diagonal flows on homogeneous spaces,
including both the rigidity theorems of such flows and their applications to orbits of arithmetic interest,
in particular CM points and integer points on spheres.
I hope to cover parts of the following papers:
Einsiedler, Manfred ; Lindenstrauss, Elon ; Michel, Philippe ; Venkatesh, Akshay . The distribution of closed geodesics
on the modular surface, and Duke's theorem. Enseign. Math. (2) 58 (2012), no. 3-4, 249--313.
Einsiedler, M., Lindenstrauss, E., Symmetry of entropy in higher rank diagonalizable actions and measure classification.
arXiv e-prints arXiv:1803.07762.
Einsiedler, M. & Lindenstrauss, E. .Joinings of higher rank torus actions on homogeneous spaces. Publ.math.IHES (2019).
<a href="https://doi.org/10.1007/s10240-019-00103-y">https://doi.org/10.1007/s10240-019-00103-y</a>
Khayutin, Ilya . Joint equidistribution of CM points. Ann. of Math. (2) 189 (2019), no. 1, 145--276.
Aka, Menny ; Einsiedler, Manfred ; Shapira, Uri . Integer points on spheres and their orthogonal lattices.
Invent. Math. 206 (2016), no. 2, 379--396.Sun, 27 Oct 2019 09:00:00 +0000Anonymous92997 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil?delta=12" >Kazhdan Sunday seminar: "Computation, quantumness, symplectic geometry, and information" (Gil Kalai, Leonid Polterovich, with participation of Dorit Aharonov and Guy Kindler)</a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil
Tentative syllabus
1. Mathematical models of classical and quantum mechanics.
2. Correspondence principle and quantization.
3. Classical and quantum computation: gates, circuits, algorithms
(Shor, Grover). Solovay-Kitaev. Some ideas of cryptography
4. Quantum noise and measurement, and rigidity of the Poisson bracket.
5. Noisy classical and quantum computing and error correction, threshold theorem- quantum fault tolerance (small noise is good for quantum computation). Kitaev's surface code.
6. Quantum speed limit/time-energy uncertainty vs symplectic displacement energy.
7. Time-energy uncertainty and quantum computation (Dorit or her student?)
8. Berezin transform, Markov chains, spectral gap, noise.
9. Adiabatic computation, quantum PCP (probabilistically checkable proofs) conjecture
[? under discussion]
10. Noise stability and noise sensitivity of Boolean functions, noisy boson
sampling
11. Connection to quantum field theory (Guy?).
Literature:
Aharonov, D. Quantum computation, In "Annual Reviews of Computational Physics" VI, 1999
(pp. 259-346).
<a href="https://arxiv.org/abs/quant-ph/9812037">https://arxiv.org/abs/quant-ph/9812037</a>
Kalai, G., Three puzzles on mathematics computations, and games, Proc. Int
Congress Math 2018, Rio de Janeiro, Vol. 1 pp. 551–606.
<a href="https://arxiv.org/abs/1801.02602">https://arxiv.org/abs/1801.02602</a>
Nielsen, M.A., and Chuang, I.L., Quantum computation and quantum information. Cambridge University Press, Cambridge, 2000.
Polterovich, L., Symplectic rigidity and quantum mechanics, European Congress of Mathematics, 155–179, Eur. Math. Soc., Zürich, 2018.
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rigidity-and-quantum-mechanics">https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rig...</a>
Polterovich L., and Rosen D., Function theory on symplectic manifolds. American Mathematical Society; 2014. [Chapters 1,9]
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/function-theory-on-symplectic-manifolds">https://sites.google.com/site/polterov/miscellaneoustexts/function-theor...</a>
Wigderson, A., Mathematics and computation, Princeton Univ. Press, 2019.
<a href="https://www.math.ias.edu/files/mathandcomp.pdf">https://www.math.ias.edu/files/mathandcomp.pdf</a>Sun, 27 Oct 2019 12:00:00 +0000Anonymous92999 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze?delta=12" >Kazhdan Sunday seminar: Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze) </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze
Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze)
Abstract: We shall discuss (Weil) cohomology theories for algebraic varieties.
When working with schemes over p-complete rings and taking cohomologies with p-complete coefficients one gets a plurality of such cohomology theories (e'tale, De-Rahm, Crystalline, etc.. ). The comparison between these different cohomology theories is a subtle subject known as "p-adic hodge theory" .
Recently Bhatt and Scholze defined a new such cohomology theory called prismatic cohomology. Remarkably, prismatic cohomology is easier to define than most p-adic cohomology theories and in the same specialized to each of them.The main new tool is the notions of delta-rings and prisms.
We shall start discussing general Weil) cohomology theories for algebraic varieties and give basic examples, we then move to develop the algebra of delta-rings and prisms, we then define the prisamtic site and prismatic cohomology. We shall then continue with comparison theorems and finally some applications Sun, 27 Oct 2019 14:00:00 +0000Anonymous92998 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows?delta=13" >Kazhdan Sunday seminar: Elon Lindenstrauss "Arithmetic applications of diagonal flows" </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows
Elon Lindenstrauss "Arithmetic applications of diagonal flows"
I will give an introduction to the dynamics of higher rank diagonal flows on homogeneous spaces,
including both the rigidity theorems of such flows and their applications to orbits of arithmetic interest,
in particular CM points and integer points on spheres.
I hope to cover parts of the following papers:
Einsiedler, Manfred ; Lindenstrauss, Elon ; Michel, Philippe ; Venkatesh, Akshay . The distribution of closed geodesics
on the modular surface, and Duke's theorem. Enseign. Math. (2) 58 (2012), no. 3-4, 249--313.
Einsiedler, M., Lindenstrauss, E., Symmetry of entropy in higher rank diagonalizable actions and measure classification.
arXiv e-prints arXiv:1803.07762.
Einsiedler, M. & Lindenstrauss, E. .Joinings of higher rank torus actions on homogeneous spaces. Publ.math.IHES (2019).
<a href="https://doi.org/10.1007/s10240-019-00103-y">https://doi.org/10.1007/s10240-019-00103-y</a>
Khayutin, Ilya . Joint equidistribution of CM points. Ann. of Math. (2) 189 (2019), no. 1, 145--276.
Aka, Menny ; Einsiedler, Manfred ; Shapira, Uri . Integer points on spheres and their orthogonal lattices.
Invent. Math. 206 (2016), no. 2, 379--396.Sun, 27 Oct 2019 09:00:00 +0000Anonymous92997 at https://mathematics.huji.ac.il